Tiêu đề 04. Quadratic Equations Easy.pdf ✅

1.)The roots of the equation ( 1) ( 1) 0 2 2 a x + − a + x = are (a.) a a 1 , (b.) a, 2a (c.) a a 2 1 , (d.) None of these 2.)The roots of the equation 8 9 0 4 2 x − x − = are (a.) 3, 1 (b.) 3,  i (c.) 2,  i (d.) None of these 3.)The roots of the equation 4 4 0 2 ix − x − i = are (a.) −2i (b.) 2i (c.) −2i,−2i (d.) 2i,2i 4.)The roots of the equation 2 0 2 / 3 1 / 3 x + x − = are (a.) 1, 4 (b.) 1,−4 (c.) 1,−8 (d.) 1, 8 5.)If 2 2 2 , 2 / 3 1 / 3 x = + + then x − 6x + 6x = 3 2 (a.) 3 (b.) 2 (c.) 1 (d.) None of these 6.)The number of roots of the quadratic equation 8 sec 6 sec 1 0 2  −  + = is (a.) Infinite (b.) 1 (c.) 2 (d.) 0 7.)The roots of the equation 3x +1 +1 = x are (a.) 0 (b.) 1 (c.) 0, 1 (d.) None 8.)The number which exceeds its positive square root by 12 is (a.) 9 (b.) 16 (c.) 25 (d.) None of these 9.)The roots of the equation 3 10 .3 9 2 − + x x =0 are (a.) 1, 2 (b.) 0, 2 (c.) 0, 1 (d.) 1, 3 10.)If 7 10 0, 2 / 3 1 / 3 x − x + = then x =
(a.) {125} (b.) {8} (c.)  (d.) {125, 8} 11.)If 25, 12 2 2 x + y = xy = , then x = (a.) {3, 4} (b.) {3, –3} (c.) {3, 4, –3, –4} (d.) {–3, –3} 12.)The solution set of the equation 9 2 log (1 ) = −x x x is (a.) {– 2, 4} (b.) {4} (c.) {0, – 2, 4} (d.) None of these 13.)Let one root of 0 2 ax + bx + c = where a,b, c are integers be 3 + 5 , then the other root is (a.) 3 − 5 (b.) 3 (c.) 5 (d.) None of these 14.)The number of real solutions of the equation 2 | x | – 3| x | +2 = 0 are (a.) 1 (b.) 2 (c.) 3 (d.) 4 15.)The number of real roots of the equation 4 sin sin − − x − x e e = 0 are (a.) 1 (b.) 2 (c.) Infinite (d.) None 16.)The number of real solutions of the equation | 2 x + 4x + 3| + 2x + 5 = 0 are (a.) 1 (b.) 2 (c.) 3 (d.) 4 17.)The roots of the given equation ( ) ( ) ( ) 0 2 p − q x + q − r x + r − p = are (a.) ,1 r p p q − − (b.) ,1 p q q r − − (c.) ,1 p q r p − − (d.) p q q r − − 1, 18.)If a root of the equation 12 0 2 x + px + = is 4, while the roots of the equation 0 2 x + px + q = are same, then the value of q will be (a.) 4 (b.) 4/49 (c.) 49/4
(d.) None of these 19.)How many roots the equation 1 2 1 1 2 − = − − − x x x have (a.) One (b.)Two (c.) Infinite (d.) None 20.)The solution of the equation 2 1 + = x x will be (a.) 2, –1 (b.) 0, –1, 5 1 − (c.) 5 1 −1,− (d.) None of these 21.)If the product of the roots of the equation 2x + 6 x + 2 1 0 2  + = is − , then the value of  will be (a.) –1 (b.) 1 (c.) 2 (d.) –2 22.)If 3 7 30 2 7 5 5 2 2 x − x − + x − x − = x + ,then x is equal to (a.) 2 (b.) 3 (c.) 6 (d.) 5 23.)The value of +  + + 2 .......... . 1 2 1 2 is (a.) 1 − 2 (b.) 1 + 2 (c.) 1  2 (d.) None of these 24.)The roots of the equation 2 27 9 2 /( 1) = x+ x x− are given by (a.) 1 − log2 3, 2 (b.) , 1 3 2 log2       (c.) 2,−2 (d.) log 2 log 3 − 2, 1 − 25.)Let  and  be the roots of the equation 1 0 2 x + x + = The equation whose roots are 19 7  ,  is (a.) 1 0 2 x − x − = (b.) 1 0 2 x − x + = (c.) 1 0 2 x + x − = (d.) 1 0 2 x + x + = 26.)If | x − 2| +| x − 3|= 7 , then x = (a.) 6 (b.) –1 (c.) 6 or –1
(d.) None of these 27.)If 1 2 3 x , x , x are distinct roots of the equation 0 2 ax + bx + c = then (a.) a = b = 0, c  R (b.) a = c = 0,b  R (c.) 4 0 2 b − ac  (d.) a = b = c = 0 28.)The number of roots of the equation | | 7| | 12 0 2 x − x + = is (a.) 1 (b.) 2 (c.) 3 (d.) 4 29.)The number of solutions of 2 log( 2) log 5 log( 1) 2 = − + + x x is (a.) 2 (b.) 3 (c.) 1 (d.) None of these 30.)If x = 7 + 4 3 , then + = x x 1 (a.) 4 (b.) 6 (c.) 3 (d.) 2 31.)If log log 2 3 10 log2 log x 2 2 y x + = = y + and x  y, then x + y = (a.) 2 (b.) 65/8 (c.) 37/6 (d.) None of these 32.)The value of x = 2 + 2 + 2 + ..... is (a.) –1 (b.) 1 (c.) 2 (d.) 3 33.)The value of x in the given equation 2 2 1 1 2 1 4 3 3 2 − − + − = − x x x x is (a.) 3 4 (b.) 2 3 (c.) 1 2 (d.) 3 5 34.)The equation e − x −1 = 0 x has (a.) Only one real root x = 0 (b.) At least two real roots